2017/12/02 by Alec Rhea, Rhea, Alec
Computer Science · Mathematics · #12-XX #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Mathematical and Theoretical Analysis #Polynomial and algebraic computation #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1712.00662
openalex publication_date 2017/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper I generalize the notion of a polynomial over an ordered field to that of a naked polynomial over a non-Archimedean ordered field, subsequently showing that the notion of a naked polynomial ring forms an Euclidean domain. This canonically generalizes the methods of Galois theory of fields and polynomial rings to a transfinite Galois theory of non-Archimedean ordered fields and naked polynomial rings, lifting the processes of splitting and algebraic closure to non-Archimedean ordered fields.